QuestionWhat is the probability of drawing a heart or an ace from a standard deck of cards? Round your answer to three decimal places.
Studdy Solution
STEP 1
Assumptions1. An ordinary deck of playing cards has52 cards.
. There are4 suits in a deck of cards hearts, diamonds, clubs, and spades. Each suit has13 cards.
3. There are4 aces in a deck of cards, one for each suit.
STEP 2
First, let's calculate the probability of drawing a heart. This is the number of hearts divided by the total number of cards.
STEP 3
Now, plug in the known values to calculate the probability of drawing a heart.
STEP 4
implify the fraction to get the probability of drawing a heart.
STEP 5
Next, let's calculate the probability of drawing an ace. This is the number of aces divided by the total number of cards.
STEP 6
Now, plug in the known values to calculate the probability of drawing an ace.
STEP 7
implify the fraction to get the probability of drawing an ace.
STEP 8
We want to find the probability of drawing a heart or an ace. However, we must consider that there is an overlap in these two events the ace of hearts is both a heart and an ace. So we must subtract the probability of this overlap from the sum of the individual probabilities.
STEP 9
The probability of drawing the ace of hearts (which is both a heart and an ace) is out of52.
STEP 10
Now, plug in the calculated probabilities to find the probability of drawing a heart or an ace.
STEP 11
To add or subtract fractions, they must have the same denominator. Let's find a common denominator for these fractions.
STEP 12
Convert each fraction to have the common denominator of52.
STEP 13
Now, add and subtract the fractions to get the final probability.
STEP 14
implify the fraction to get the final probability.
The probability that the card is a heart or ace is4/13.
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